本文關(guān)鍵詞：表面粗化處理不均衡螺紋鈦人工牙種植體的生物學性能研究　出處：《河北醫(yī)科大學》2017年博士論文　論文類型：學位論文

  更多相關(guān)文章： 鈦人工牙種植體 不均衡螺紋 頸部微螺紋 鈦顆粒噴砂 熱酸蝕 三維有限元 疲勞性能 骨結(jié)合

【摘要】：第一部分不均衡螺紋鈦人工牙種植體的三維有限元應力分析目的:在種植體生物力學優(yōu)化設計中螺紋形態(tài)扮演了非常重要的角色,它可以增加種植體-骨接觸面積,提高種植體初始穩(wěn)定性,改善骨界面的應力分布。目前骨內(nèi)種植體表面螺紋多采用均衡分布的單一螺紋,而針對骨皮質(zhì)區(qū)采用節(jié)距及深度較小的微螺紋、骨松質(zhì)區(qū)采用節(jié)距相對較寬的螺紋,有文獻證實這種不均衡螺紋設計有較好的力學效應,但是對于頸部不同微螺紋的生物力學特性很少有報道。正確設計種植體的形狀,使種植體與骨組織之間的界面上受力盡量趨于合理,尤其是降低頸部皮質(zhì)骨上緣處的應力集中,將有助于減少骨吸收,降低種植體發(fā)生松動的可能性,延長其使用壽命。為提高種植修復的遠期成功率,有必要進行種植體螺紋的優(yōu)化設計,尤其是頸部微螺紋結(jié)構(gòu)的優(yōu)化及螺紋的優(yōu)化組合。本實驗旨在探討不同頸部螺紋外形設計種植體的生物力學性能。方法:1種植體分組四種不同頸部形態(tài)分為均衡螺紋組、寬頸組、頸部單頭微螺紋組、頸部雙頭微螺紋組。2下頜骨模型2.1初步建模依據(jù)頭顱CT掃描圖像,在Mimics 16.0中建立對應新項目。根據(jù)CT圖像灰度值將骨質(zhì)部分提取出來,對骨質(zhì)物蒙罩進行編輯,得到精確的僅包括下頜骨像素點的無空隙蒙罩模型,由蒙罩內(nèi)像素點自動計算三維模型,將最終生成的下頜骨初步三維幾何模型以STL(Standard Template Library)格式輸出。2.2模型優(yōu)化將STL格式的下頜骨初步三維模型導入到Geomagic studio 2013中,采用多次快速光順將模型初步光滑化,改善多邊形曲面性能,獲得下頜骨多邊形模型,轉(zhuǎn)到精確曲面階段,獲得下頜骨曲面片模型。經(jīng)過CAD對象轉(zhuǎn)換,最終得到下頜骨CAD模型。2.3生成皮質(zhì)骨與松質(zhì)骨在Geomagic多邊形階段,通過向內(nèi)1.5mm抽殼并刪除交叉面得到下頜骨的皮質(zhì)骨與松質(zhì)骨交界面的多邊形模型,再按上述步驟逐步操作得到以交界面為外輪廓的松質(zhì)骨CAD模型。將已得到的下頜骨整體CAD模型和松骨質(zhì)CAD模型導入到Solidworks 2015中,由布爾減操作,即得到皮質(zhì)骨模型。2.4種植體與下頜骨的裝配分別將四組種植體置于下頜骨第一磨牙區(qū)某一相同位置,由Solidworks在種植體頂部建立高度為3.2mm的基臺,在其上建立頂端為2mm厚度的瓷修復體。將其以sat格式導入Ansys Workbench 14.5中。2.5網(wǎng)格劃分采用以六面體為主四面體為輔的自動網(wǎng)格劃分方法,單元大小約為0.5mm,在種植體及其附近節(jié)點和單元適當加密。2.6材料屬性及約束所有材料假設為均質(zhì)各向同性的線彈性材料,材料變形為彈性小變形。將下頜骨兩側(cè)髁突頂端所有節(jié)點自由度予以剛性約束;種植體與骨組織為100%骨結(jié)合;瓷修復體和種植體之間為固定接觸。2.7加載條件分別施加以下三種載荷工況的均布載荷:軸向100N、由頰側(cè)向舌側(cè)水平50N、與種植體軸線成30°由唇頰側(cè)指向舌側(cè)向下100N。2.8評價指標分析Von-Mises等效應力和最大主應力。結(jié)果:1種植體-骨界面應力分布總的特征種植體頸部不同特征對種植體-骨界面應力值、應力分布有明顯影響;整體應力集中區(qū)域均位于種植體的頸部及種植體根尖部。2軸向加載100牛頓時對于均衡螺紋組、寬頸組、頸部單頭微螺紋組、頸部雙頭微螺紋組而言,皮質(zhì)骨區(qū)等效應力最大值分別為46.58MPa、35.25MPa、20.98MPa、58.01MPa,松質(zhì)骨區(qū)等效應力最大值分別為3.64MPa、7.45MPa、2.60MPa、12.38MPa。對于這四組種植體而言,在皮質(zhì)骨上緣處的最大主應力值分別為0.97MPa、0.89MPa、0.79MPa、1.22MPa;在皮質(zhì)骨與松質(zhì)骨交界處的最大主應力值分別為1.72MPa、3.89MPa、0.45MPa、8.07MPa;在種植體的末端處的最大主應力值分別為0.73MPa、0.67MPa、0.64MPa、0.57MPa;四組種植體在松質(zhì)骨區(qū)中段位點的最大主應力值均表現(xiàn)為較低水平。3頰舌向水平加載50牛頓時對于均衡螺紋組、寬頸組、頸部單頭微螺紋組、頸部雙頭微螺紋組而言,皮質(zhì)骨區(qū)等效應力最大值分別為53.21MPa、41.93MPa、36.95MPa、64.18MPa,松質(zhì)骨區(qū)等效應力最大值分別為3.72MPa、6.57MPa、3.77MPa、4.07MPa。對于這四組種植體而言,在皮質(zhì)骨上緣處的最大主應力值分別為41.77MPa、39.61MPa、29.67MPa、46.99MPa;在皮質(zhì)骨與松質(zhì)骨交界處的最大主應力值分別為9.45MPa、2.80MPa、1.73MPa、9.49MPa;在種植體的末端處的最大主應力值分別為0.07MPa、0.09MPa、0.15MPa、0.26MPa;四組種植體在皮質(zhì)骨區(qū)的最大主應力值均表現(xiàn)為較高水平。4斜向加載100牛頓時對于均衡螺紋組、寬頸組、頸部單頭微螺紋組、頸部雙頭微螺紋組而言,皮質(zhì)骨區(qū)等效應力最大值分別為49.37MPa、47.78MPa、34.02MPa、78.52MPa,松質(zhì)骨區(qū)等效應力最大值分別為3.74MPa、3.72MPa、3.81MPa、7.33MPa。對于這四組種植體而言,在皮質(zhì)骨上緣處的最大主應力值分別為29.35MPa、21.28MPa、15.34MPa、34.69MPa;在皮質(zhì)骨與松質(zhì)骨交界處的最大主應力值分別為3.50MPa、2.71MPa、0.97MPa、8.58MPa;在種植體的末端處的最大主應力值分別為0.16MPa、0.11MPa、0.15MPa、0.10MPa;四組種植體在皮質(zhì)骨區(qū)的最大主應力值均表現(xiàn)為較高水平。第二部分表面粗化處理不均衡螺紋鈦人工牙種植體的疲勞性能研究目的:人工牙種植體的材料及其表面性狀、形態(tài)是影響骨整合的重要因素。噴砂+酸蝕表面處理技術(shù)是一種新型非涂層鈦牙種植體表面改性方法。經(jīng)該方法處理的鈦種植體表面,其形貌特征發(fā)生了明顯的改變,不僅使其表面的粗糙度明顯提高,且優(yōu)化了種植體表面的超微結(jié)構(gòu);酸化處理后,大的孔洞中形成了無數(shù)微小的二級窩洞,這對提高骨組織與種植體表面之間的機械鎖合有重要的意義。鈦顆粒噴砂消除了異種元素的污染,HCL/H2SO4混合酸熱處理噴砂后的表面,獲得了較為理想的表面形貌特征,但該物理、化學處理工藝對種植體疲勞性能的影響程度如何,未見有報道。本實驗旨在探討種植體不同頸部螺紋外形設計及表面粗化處理對力學疲勞性能的影響。方法:1種植體分組分為均衡螺紋組、寬頸組、頸部單頭微螺紋組、頸部雙頭微螺紋組、表面粗化及頸部雙頭微螺紋組。2表面形貌觀察頸部雙頭微螺紋組、表面粗化及頸部雙頭微螺紋組經(jīng)FSEM觀察分析種植體表層的結(jié)構(gòu)、形貌。3疲勞試驗3.1試驗標準依據(jù)IS014801:2007加載3.2試驗環(huán)境在空氣中進行,溫度20±5℃3.3載荷波形和頻率采用單向載荷,載荷在標稱峰值和10%標稱峰值之間呈正弦曲線變化;載荷頻率為15Hz。3.4步驟3.4.1種植體各組件的組裝下部結(jié)構(gòu)、基臺通過內(nèi)六方連接,由中央螺栓緊固8-10Ncm。3.4.2半球形承載部件的粘接3.4.3種植體的包埋及固定3.4.4連接INSTRON電子動靜態(tài)萬能材料試驗機3.4.5初始載荷為靜態(tài)載荷值的80%,隨后依次降低,每個試驗組至少測試四個不同載荷,直至達到5×10~6循環(huán)時測得的最大耐受,在此載荷下三個試件完好。3.4.6計算施加的最大彎矩3.4.7記錄在各載荷下的循環(huán)次數(shù)及位移,比較在同一加載力值下達到5×10~6循環(huán)的位移。結(jié)果:1表面形貌觀察頸部雙頭微螺紋組的Ma表面,肉眼觀:表面光滑、潔凈,色澤均勻發(fā)亮呈金屬銀白色。FSEM觀察:低倍電鏡下,表面平整、微粗糙,可見方向一致的條紋。300倍電鏡下,表面較多平行排列的切削溝紋,微粗糙;千倍以上電鏡下可以看到表面較平整,有大量方向一致的、規(guī)則的、淺溝紋狀的切削條痕,局部散在點狀凹陷及凸起。表面粗化及頸部雙頭微螺紋組的SLA粗化表面,肉眼觀:表面粗糙,不見金屬色澤,呈均勻的灰白色。FSEM觀察:低倍電鏡下,表面整潔、粗糙均勻;300倍電鏡下,呈現(xiàn)不規(guī)則的粗糙表面,可見淺凹及小的裂隙;千倍電鏡下可見不規(guī)則的凹陷表面上有大量大小不一的微孔;微孔大小為5-30um,邊緣銳利,相鄰微孔部分融合,偶爾可見散在的微裂隙;萬倍電鏡下,在大的窩洞、凹陷內(nèi)還可以看到大量形狀不規(guī)則的小的凹坑,約200-500nm,大小、深淺不一,洞底為半圓形,邊緣圓鈍。2動態(tài)循環(huán)疲勞性能2.1種植體達到5×10~6循環(huán)的極限載荷及最大彎矩均衡螺紋組、寬頸組、頸部單頭微螺紋組、頸部雙頭微螺紋組、表面粗化及頸部雙頭微螺紋組種植體達到5×10~6循環(huán)的極限載荷值分別為250N、300N、300N、300N、275N;對應的最大彎矩為137.50Ncm、165.00Ncm、165.00Ncm、165.00Ncm、151.25Ncm。2.2種植體動態(tài)疲勞位移均衡螺紋組、寬頸組、頸部單頭微螺紋組、頸部雙頭微螺紋組、表面粗化及頸部雙頭微螺紋組種植體在250N載荷下,達到5×10~6循環(huán)時,對應的位移分別為0.391mm、0.251mm、0.257mm、0.258mm、0.272mm。第三部分表面粗化處理不均衡螺紋鈦人工牙種植體的骨結(jié)合性能研究目的:實驗一探討了種植體不同頸部外形對應力分布的影響,實驗二探討了種植體不同頸部螺紋外形設計及表面粗化處理對力學疲勞性能的影響。本研究旨在探討種植體不同頸部螺紋外形設計及表面粗化處理對骨結(jié)合性能的影響,為優(yōu)化種植體頸部微螺紋結(jié)構(gòu)及粗化表面設計提供較為完整的實驗依據(jù)。方法:1實驗動物分組成年新西蘭大白兔90只,雄性,隨機分為五組,均衡螺紋組、寬頸組、頸部單頭微螺紋組、頸部雙頭微螺紋組、表面粗化及頸部雙頭微螺紋組,每組18只。2種植體植入手術(shù)動物術(shù)前6小時禁食、禁飲,1%戊巴比妥鈉注射液經(jīng)耳緣靜脈麻醉;在兔股骨的遠心末端術(shù)區(qū)備皮,消毒,鋪巾;用0.5%鹽酸利多卡因注射液局部浸潤麻醉;依次切開皮膚、筋膜和骨膜,剝離骨膜暴露骨面,用系列擴孔鉆依次制備植入窩洞。將五組種植體隨機植入每只動物的股骨遠心末端,植入扭矩10Ncm,植入體頂端與骨面平齊,創(chuàng)口局部用0.9%氯化鈉注射液沖洗,依次縫合骨膜、筋膜、皮膚。3 X-ray平片觀察術(shù)后12周時,拍攝X-ray平片觀察五組標本的影像學特點。4旋出扭矩測試術(shù)后4周、8周和12周時,分別處死五組動物,取下帶有種植體的股骨,采用便攜式數(shù)字扭矩測試儀測量旋出種植體時的最大扭矩值。5種植體-骨界面的掃描電鏡觀察術(shù)后4周、8周和12周時,將頸部雙頭微螺紋組、表面粗化及頸部雙頭微螺紋組旋出的種植體固定、脫水、干燥、粘臺、噴金,用FSEM觀察種植體表面形貌特點。6種植體-骨界面的能譜分析術(shù)后4周、8周和12周時,將頸部雙頭微螺紋組、表面粗化及頸部雙頭微螺紋組旋出的種植體干燥、粘臺、噴金,用EDX測試種植體-骨界面化學元素組成。7組織學觀察將術(shù)后12周取下的頸部雙頭微螺紋組、表面粗化及頸部雙頭微螺紋組帶有種植體的股骨標本脫礦制作組織切片,HE染色,觀察骨結(jié)合情況。8統(tǒng)計學分析五組的旋出扭矩值采用SPSS20.0軟件包處理,采用重復測量資料方差分析,P0.05時具有統(tǒng)計學意義。結(jié)果:1 X-ray平片觀察術(shù)后12周時,各種植體周圍界面無透射線性影像,與周圍骨的密度比較相似;各種植體頸部周圍未見明顯骨吸收影響。2旋出扭矩在4、8、12周時,表面粗化及頸部雙頭微螺紋組的旋出扭矩值均較頸部雙頭微螺紋組高;頸部單頭微螺紋組、頸部雙頭微螺紋組旋出扭矩值無明顯差別,均高于均衡螺紋組、寬頸組的旋出扭矩值;寬頸組最低。3 FSEM觀察3.1術(shù)后4周頸部雙頭微螺紋組種植體表面覆蓋極薄層纖維組織,種植體表面機械銑削條痕尚沒有被粘附組織所覆蓋;而表面粗化及頸部雙頭微螺紋組種植體表面的粘附組織較均勻,幾乎完全覆蓋種植體表面的粗化多孔結(jié)構(gòu),可見少量骨組織。3.2術(shù)后8周頸部雙頭微螺紋組種植體表面覆蓋薄層纖維及少許骨組織,種植體表面機械銑削條痕尚沒有完全被粘附組織所覆蓋;而表面粗化及頸部雙頭微螺紋組種植體表面的粘附組織較厚,骨組織粘附于種植體表面的粗化多孔結(jié)構(gòu)。3.3術(shù)后12周頸部雙頭微螺紋組種植體表面覆蓋薄層骨組織,種植體表面機械銑削條痕幾乎完全被粘附骨組織所覆蓋,而表面粗化及頸部雙頭微螺紋組種植體表面的粘附骨組織厚,呈蜂窩狀,完全覆蓋種植體表面的粗化多孔結(jié)構(gòu)。4 EDX分析4周時頸部雙頭微螺紋組種植體表面粘附組織中鈣26.45%、磷21.29%,而在表面粗化及頸部雙頭微螺紋組種植體鈣52.26%、磷32.99%;8周時頸部雙頭微螺紋組種植體表面粘附組織中鈣37.72%、磷25.63%,而在表面粗化及頸部雙頭微螺紋組種植體鈣53.97%、磷34.39%;12周時頸部雙頭微螺紋組種植體表面粘附組織中鈣48.06%、磷32.05%,而在表面粗化及頸部雙頭微螺紋組種植體鈣54.23%、磷34.56%。5組織學觀察術(shù)后12周時,頸部雙頭微螺紋組、表面粗化及頸部雙頭微螺紋組種植體周圍可見清晰的板層狀骨,頸部雙頭微螺紋組結(jié)合骨板較薄、致密性稍低,較為連續(xù);表面粗化及頸部雙頭微螺紋組結(jié)合骨板較厚、致密,連續(xù)性好,且周圍新骨內(nèi)可見較多的骨細胞。結(jié)論:1柱狀V形螺紋種植體不同頸部形態(tài)對種植體-骨界面應力值、應力分布有影響,整體應力集中區(qū)域均位于種植體的頸部皮質(zhì)骨區(qū)及根尖部。2同一螺紋形態(tài)頸部單頭微螺紋組能夠明顯降低軸向、水平向及斜向加載時的皮質(zhì)骨區(qū)的Von-Mises等效應力、最大主應力。3寬頸組與頸部單頭微螺紋組相比,在軸向、水平向及斜向加載時的皮質(zhì)骨區(qū)的Von-Mises等效應力、最大主應力值較高。4均衡螺紋組與寬頸組相比,在軸向、水平向及斜向加載時的皮質(zhì)骨區(qū)的Von-Mises等效應力、最大主應力值較高。5同一螺紋形態(tài)頸部雙頭微螺紋組在軸向、水平向及斜向加載時的皮質(zhì)骨區(qū)的Von-Mises等效應力、最大主應力值較高。6寬頸組、頸部單頭微螺紋組、頸部雙頭微螺紋組種植體疲勞耐受性能相似,均高于均衡螺紋組。7鈦顆粒噴砂后HCL/H2SO4熱酸蝕表面種植體較機械加工表面種植體的疲勞耐受性能有所降低,但能夠滿足臨床功能狀態(tài)下的力學要求。8各觀察時間點,表面粗化及頸部雙頭微螺紋組的旋出扭矩值均較頸部雙頭微螺紋組高;頸部單頭微螺紋組與頸部雙頭微螺紋組旋出扭矩值無明顯差別,均高于均衡螺紋組和寬頸組,寬頸組最低。各組扭矩值變化趨勢大體一致,植入后8周時較4周有所升高,12周時升高明顯達到峰值。9各觀察時間點,鈦顆粒噴砂后HCL/H2SO4熱酸蝕表面種植體表面沉積的骨反應物及其中的鈣、磷含量均較機械加工表面種植體多,且形成時間較早。10植入術(shù)后12周時,鈦顆粒噴砂后HCL/H2SO4熱酸蝕表面種植體結(jié)合骨板寬度、致密性、連續(xù)性均較機械加工表面種植體好。
[Abstract]:The first part of the unbalanced threaded titanium dental implant three dimensional finite element stress analysis objective: to play a very important role in implant biomechanical optimization of thread form design, it can increase the contact area of the bone implant, improve the initial implant stability, improve the stress distribution of bone interface. The bone implant thread with single thread balanced distribution, and in the cortical area of the section of micro screw, bone length and depth of the smaller cancellous zone by pitch thread is relatively wide, literatures have confirmed that this imbalance has good effect on mechanical thread design, but is rarely reported in biomechanics the characteristics of different micro neck threads. The correct design of the shape of the implant can make the stress on the interface between implant and bone as far as possible, especially reduce the stress concentration at the upper edge of the cortical bone. It will help reduce bone resorption, reduce the possibility of loosening of implant and prolong its service life. In order to improve the long-term success rate of implant restoration, it is necessary to optimize the design of implant thread, especially the optimization of neck micro thread structure and the optimal combination of threads. The purpose of this study was to investigate the biomechanical properties of different cervical threaded designs. Methods: 1 implant groups were divided into four different neck shapes into balanced thread group, wide neck group, neck single head micro screw group, and neck double head micro thread group. 2 the model 2.1 of the mandible was modeled according to the CT scan of the head, and a new project was established in the Mimics 16. Based on CT image gray value will be part of the extract of bone, bone masks for editing, get accurate only includes void pixel mask model of mandible, automatic calculation of 3D model by pixel mask, will eventually produce the initial mandible three-dimensional geometric model with STL (Standard Template Library) format. 2.2 optimization model STL format will be a preliminary mandible three-dimensional model into Geomagic studio 2013, using several fast smoothing initial model smoothing, improve the polygonal surface performance, obtained the mandible polygon model, to obtain accurate surface phase, surface patch model of mandible. After the CAD object conversion, the CAD model of the mandible was finally obtained. 2.3, generate cortical bone and cancellous bone in the Geomagic polygon stage, and get the polygonal model of the interface between the cortical bone and cancellous bone in the mandibular bone in the Geomagic polygon stage by extracting and removing the cross faces. Then, according to the above steps, we gradually get the CAD model of the cancellous bone with the external interface as the interface. The acquired CAD model of the mandible and the CAD model of the cancellous bone were introduced into Solidworks 2015, and the cortical bone model was obtained by Boolean operation. 2.4 implant and mandible assembly, four groups of implant were placed in the same place in the first molar area of mandible, and Solidworks was set up on the top of the implant to build a 3.2mm abutment. On the top, a porcelain restoration with a thickness of 2mm was built. Import it into the Ansys Workbench 14.5 in sat format. 2.5 mesh generation is based on hexahedron and tetrahedron as an auxiliary mesh. The cell size is about 0.5mm, and it is properly encrypted for implants and adjacent nodes and units. The properties and constraints of 2.6 materials are assumed to be homogeneous isotropic linear elastic materials, and the material is deformed into small elastic deformation. The degree of freedom of all the nodes at the top of the condyle on both sides of the mandible was rigidly constrained, and the implant and bone tissue were combined with 100% bones. 2.7 loading conditions were applied to the following three load conditions: the axial load was 100N, the lateral buccal side was 50N, and the axis of the implant was 30 degrees, from the buccal side to the tongue side to the 100N. 2.8 evaluation index analysis Von-Mises equivalent stress and maximum principal stress. Results: 1, the total stress distribution characteristics of implant bone interface had different effects on implant bone interface stress value and stress distribution. The whole stress concentration area was located in the neck of implant and root tip of implant. 2 axial loading of 100 Newton for balanced thread group, wide neck group, single head neck micro thread group, double neck micro thread group, cortical bone area, the maximum equivalent stress are respectively 46.58MPa, 35.25MPa, 20.98MPa, 58.01MPa, loose bone area equivalent maximum stress value is 3.64MPa, 7.45MPa, 2.60MPa, 12.38MPa respectively. For the four groups of implants, the maximum principal in the cortical bone at the upper edge of the stress values were 0.97MPa, 0.89MPa, 0.79MPa, 1.22MPa; the maximum principal cortical and cancellous bone at the junction of the stress values were 1.72MPa, 3.89MPa, 0.45MPa, 8.07MPa; the maximum principal in at the end of the implant. The stress values were 0.73MPa, 0.67MPa, 0.64MPa, 0.57MPa; four groups of implants in the cancellous bone region of the maximum principal stress value loci showed low level. 3 buccolingual horizontal loading 50 Newton for balanced thread group, wide neck group, single head neck micro thread group, double neck micro thread group, cortical bone area, the maximum equivalent stress are respectively 53.21MPa, 41.93MPa, 36.95MPa, 64.18MPa, loose bone equivalent stress, the maximum value is 3.72MPa, 6.57MPa 3.77MPa and 4.07MPa respectively. For the four groups of implants, the maximum principal in the cortical bone at the upper edge of the stress values were 41.77MPa, 39.61MPa, 29.67MPa, 46.99MPa; the maximum principal cortical and cancellous bone at the junction of the stress values were 9.45MPa, 2.80MPa, 1.73MPa, 9.49MPa; the maximum principal in at the end of the implant. The stress values were 0.07MPa, 0.09MPa, 0.15MPa, 0.26MPa; maximum four groups of implant in cortical bone area, the stress values showed a higher level. 4 when oblique loading is 100 Newton, for the balanced screw group, wide neck group, neck single head micro thread group and neck double head micro thread group, the maximum equivalent stress of cortical bone area is 49.37MPa and 47.78MP respectively.
【學位授予單位】：河北醫(yī)科大學
【學位級別】：博士
【學位授予年份】：2017
【分類號】：R783.6

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